Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Sepitka, Peter¹  Simon Hilscher, Roman¹ 

[1] Masaryk Univ, Fac Sci, Dept Math & Stat, Kotlarska 2, CZ-61137 Brno, Czech Republic

关键词: Sturmian comparison theorem;    Linear Hamiltonian system;    Focal point;    Complete controllability;    Principal solution;    Sturm-Liouville equation;   

DOI  :  10.1016/j.jmaa.2020.124030

来源: Elsevier

【 摘 要 】

In this paper we consider two linear Hamiltonian differential systems on an open unbounded interval. We assume that the systems are completely controllable and satisfy the Sturmian majorant condition and the Legendre condition. We derive a singular Sturmian comparison theorem for the case when the minorant system has a solution, which is principal at both endpoints of the considered interval. The main result is new even for the second order differential equations and it generalizes the singular comparison theorem obtained by Aharonov and Elias (2010). We illustrate our new theory by several examples. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free